text: /*=========================================================================
  
    Program:   Visualization Toolkit
    Module:    vtkParametricFunction.h
  
    Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen 
    All rights reserved.
    See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
  
       This software is distributed WITHOUT ANY WARRANTY; without even 
       the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR 
       PURPOSE.  See the above copyright notice for more information.
  
  =========================================================================*/
  // .NAME vtkParametricFunction - abstract interface for parametric functions
  // .SECTION Description
  // vtkParametricFunction is an abstract interface for functions
  // defined by parametric mapping i.e. f(u,v,w)->(x,y,z) where 
  // u_min <= u < u_max, v_min <= v < v_max, w_min <= w < w_max. (For
  // notational convenience, we will write f(u)->x and assume that
  // u means (u,v,w) and x means (x,y,z).)
  //
  // The interface contains the pure virtual function, Evaluate(), that
  // generates a point and the derivatives at that point which are then used to
  // construct the surface. A second pure virtual function, EvaluateScalar(),
  // can be used to generate a scalar for the surface. Finally, the
  // GetDimension() virtual function is used to differentiate 1D, 2D, and 3D
  // parametric functions. Since this abstract class defines a pure virtual
  // API, its subclasses must implement the pure virtual functions
  // GetDimension(), Evaluate() and EvaluateScalar().
  //
  // This class has also methods for defining a range of parametric values (u,v,w).
  // 
  // .SECTION Thanks
  // Andrew Maclean a.maclean@cas.edu.au for creating and contributing the
  // class.
  //
  // .SECTION See Also
  // vtkParametricFunctionSource - tessellates a parametric function
  //
  // Implementations of derived classes implementing non-orentable surfaces:
  // vtkParametricBoy vtkParametricCrossCap vtkParametricFigure8Klein
  // vtkParametricKlein vtkParametricMobius vtkParametricRoman
  //
  // Implementations of derived classes implementing orientable surfaces:
  // vtkParametricConicSpiral vtkParametricDini vtkParametricEllipsoid 
  // vtkParametricEnneper vtkParametricRandomHills vtkParametricSuperEllipsoid 
  // vtkParametricSuperToroid vtkParametricTorus 
  //
  #ifndef __vtkParametricFunction_h
  #define __vtkParametricFunction_h
  
  #include "vtkObject.h"
  
  class VTK_COMMON_EXPORT vtkParametricFunction : public vtkObject
  {
  public:
    vtkTypeRevisionMacro(vtkParametricFunction, vtkObject);
    void PrintSelf(ostream& os, vtkIndent indent);
  
    // Description
    // Return the dimension of parametric space. Depending on the dimension,
    // then the (u,v,w) parameters and associated information (e.g., derivates)
    // have meaning. For example, if the dimension of the function is one, then
    // u[0] and Duvw[0...2] have meaning.
    // This is a pure virtual function that must be instantiated in 
    // a derived class. 
    virtual int GetDimension() = 0;
  
    // Description:
    // Performs the mapping \$f(uvw)->(Pt,Duvw)\$f.
    // This is a pure virtual function that must be instantiated in 
    // a derived class. 
    //
    // uvw are the parameters, with u corresponding to uvw[0],
    // v to uvw[1] and w to uvw[2] respectively. Pt is the returned Cartesian point, 
    // Duvw are the derivatives of this point with respect to u, v and w.  
    // Note that the first three values in Duvw are Du, the next three are Dv, 
    // and the final three are Dw. Du Dv Dw are the partial derivatives of the 
    // function at the point Pt with respect to u, v and w respectively.
    virtual void Evaluate(double uvw[3], double Pt[3], double Duvw[9]) = 0;
  
    // Description:
    // Calculate a user defined scalar using one or all of uvw, Pt, Duvw.
    // This is a pure virtual function that must be instantiated in 
    // a derived class. 
    //
    // uvw are the parameters with Pt being the the cartesian point, 
    // Duvw are the derivatives of this point with respect to u, v, and w.
    // Pt, Duvw are obtained from Evaluate().
    virtual double EvaluateScalar(double uvw[3], double Pt[3], double Duvw[9]) = 0;
  
    // Description:
    // Set/Get the minimum u-value.
    vtkSetMacro(MinimumU,double);
    vtkGetMacro(MinimumU,double);
  
    // Description:
    // Set/Get the maximum u-value.
    vtkSetMacro(MaximumU,double);
    vtkGetMacro(MaximumU,double);
  
    // Description:
    // Set/Get the minimum v-value.
    vtkSetMacro(MinimumV,double);
    vtkGetMacro(MinimumV,double);
  
    // Description:
    // Set/Get the maximum v-value.
    vtkSetMacro(MaximumV,double);
    vtkGetMacro(MaximumV,double);
  
    // Description:
    // Set/Get the minimum w-value.
    vtkSetMacro(MinimumW,double);
    vtkGetMacro(MinimumW,double);
  
    // Description:
    // Set/Get the maximum w-value.
    vtkSetMacro(MaximumW,double);
    vtkGetMacro(MaximumW,double);
  
    // Description:
    // Set/Get the flag which joins the first triangle strip to the last one.
    vtkSetMacro(JoinU,int);
    vtkGetMacro(JoinU,int);
    vtkBooleanMacro(JoinU,int);
  
    // Description:
    // Set/Get the flag which joins the the ends of the triangle strips.
    vtkSetMacro(JoinV,int);
    vtkGetMacro(JoinV,int);
    vtkBooleanMacro(JoinV,int);
  
    // Description:
    // Set/Get the flag which joins the first triangle strip to 
    // the last one with a twist.
    // JoinU must also be set if this is set. Used when building
    // some non-orientable surfaces.
    vtkSetMacro(TwistU,int);
    vtkGetMacro(TwistU,int);
    vtkBooleanMacro(TwistU,int);
  
    // Description:
    // Set/Get the flag which joins the ends of the 
    // triangle strips with a twist.
    // JoinV must also be set if this is set. Used when building
    // some non-orientable surfaces.
    vtkSetMacro(TwistV,int);
    vtkGetMacro(TwistV,int);
    vtkBooleanMacro(TwistV,int);
  
    // Description:
    // Set/Get the flag which determines the ordering of the the 
    // vertices forming the triangle strips. The ordering of the 
    // points being inserted into the triangle strip is important 
    // because it determines the direction of the normals for the 
    // lighting. If set, the ordering is clockwise, otherwise the
    // ordering is anti-clockwise. Default is true (i.e. clockwise
    // ordering).
    vtkSetMacro(ClockwiseOrdering,int);
    vtkGetMacro(ClockwiseOrdering,int);
    vtkBooleanMacro(ClockwiseOrdering,int);
  
    // Description:
    // Set/Get the flag which determines whether derivatives are available 
    // from the parametric function (i.e., whether the Evaluate() method 
    // returns valid derivatives).
    vtkSetMacro(DerivativesAvailable,int);
    vtkGetMacro(DerivativesAvailable,int);
    vtkBooleanMacro(DerivativesAvailable,int);
  
  protected:
    vtkParametricFunction();
    virtual ~vtkParametricFunction();
  
    // Variables
    double MinimumU;
    double MaximumU;
    double MinimumV;
    double MaximumV;
    double MinimumW;
    double MaximumW;
  
    int JoinU;
    int JoinV;
    int JoinW;
  
    int TwistU;
    int TwistV;
    int TwistW;
  
    int ClockwiseOrdering;
    
    int DerivativesAvailable;
  
  private:
    vtkParametricFunction(const vtkParametricFunction&);  // Not implemented.
    void operator=(const vtkParametricFunction&);  // Not implemented.
  
  };
  
  #endif
  